| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 15250.5-a1 |
15250.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{7} \cdot 5^{11} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.487421999$ |
1.487421999 |
\( \frac{758131}{4880} a + \frac{8477283}{4880} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 20 i + 6\) , \( 18 i + 8\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(20i+6\right){x}+18i+8$ |
| 15250.5-b1 |
15250.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{16} \cdot 5^{23} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.174918828$ |
1.749188287 |
\( \frac{1479632315329}{38125000000} a - \frac{155681515697137}{152500000000} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -1242 i - 231\) , \( -24076 i + 14207\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+\left(-1242i-231\right){x}-24076i+14207$ |
| 15250.5-b2 |
15250.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{8} \cdot 5^{25} \cdot 61^{2} \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.087459414$ |
1.749188287 |
\( -\frac{49764070512251349991}{363378906250000} a + \frac{496589835595616692069}{181689453125000} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -23242 i - 4231\) , \( -1206076 i + 690207\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+\left(-23242i-4231\right){x}-1206076i+690207$ |
| 15250.5-c1 |
15250.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{28} \cdot 5^{15} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 7 \) |
$0.283804959$ |
$0.259291487$ |
4.120939764 |
\( -\frac{134421165211}{3904000000} a + \frac{24723266109233}{15616000000} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 231 i + 643\) , \( -1464 i - 1557\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(231i+643\right){x}-1464i-1557$ |
| 15250.5-c2 |
15250.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{14} \cdot 5^{21} \cdot 61^{2} \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 7 \) |
$0.567609918$ |
$0.129645743$ |
4.120939764 |
\( -\frac{15137784998904637751}{58140625000000} a + \frac{19883457514836904489}{116281250000000} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 1511 i + 7683\) , \( -257720 i + 77035\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(1511i+7683\right){x}-257720i+77035$ |
| 15250.5-d1 |
15250.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{2} \cdot 5^{9} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.144115105$ |
$2.436607209$ |
4.213822872 |
\( \frac{1637458}{305} a + \frac{993713}{610} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -11 i - 4\) , \( -15 i\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-11i-4\right){x}-15i$ |
| 15250.5-e1 |
15250.5-e |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2 \cdot 5^{11} \cdot 61^{5} \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.2 |
$1$ |
\( 5 \) |
$1$ |
$0.523238224$ |
2.616191120 |
\( -\frac{14362283266683}{8445963010} a - \frac{4028212136069}{8445963010} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -160 i - 47\) , \( -1048 i + 37\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-160i-47\right){x}-1048i+37$ |
| 15250.5-e2 |
15250.5-e |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{5} \cdot 5^{7} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$2.616191120$ |
2.616191120 |
\( \frac{3415336683}{1525000} a + \frac{13679218069}{1525000} \) |
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( 5 i + 9\) , \( -8 i + 8\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(5i+9\right){x}-8i+8$ |
| 15250.5-f1 |
15250.5-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{4} \cdot 5^{5} \cdot 61^{3} \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.296995162$ |
$0.640396656$ |
4.564673011 |
\( \frac{2412612170774813}{4539620} a - \frac{197118882978304}{1134905} \) |
\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( -707 i + 403\) , \( 36 i - 8596\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-707i+403\right){x}+36i-8596$ |
| 15250.5-f2 |
15250.5-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{12} \cdot 5^{7} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.098998387$ |
$1.921189969$ |
4.564673011 |
\( \frac{126711067}{488000} a - \frac{3148217}{15250} \) |
\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( -7 i + 3\) , \( -4 i - 16\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-7i+3\right){x}-4i-16$ |
| 15250.5-g1 |
15250.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{8} \cdot 5^{13} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.760756446$ |
3.043025785 |
\( \frac{88647880993}{381250} a - \frac{504879106567}{3050000} \) |
\( \bigl[1\) , \( 1\) , \( i\) , \( -35 i - 221\) , \( 286 i + 1167\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-35i-221\right){x}+286i+1167$ |
| 15250.5-g2 |
15250.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{2} \cdot 5^{19} \cdot 61^{4} \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.190189111$ |
3.043025785 |
\( -\frac{247361637305780899}{5408531640625} a - \frac{782011543349473639}{10817063281250} \) |
\( \bigl[i\) , \( -1\) , \( 1\) , \( -2895 i - 451\) , \( 53744 i - 31877\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2895i-451\right){x}+53744i-31877$ |
| 15250.5-g3 |
15250.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{4} \cdot 5^{20} \cdot 61^{2} \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.380378223$ |
3.043025785 |
\( -\frac{7621558587291}{36337890625} a + \frac{42565044235277}{145351562500} \) |
\( \bigl[i\) , \( -1\) , \( 1\) , \( -115 i - 161\) , \( 606 i - 2011\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-115i-161\right){x}+606i-2011$ |
| 15250.5-g4 |
15250.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
15250.5 |
\( 2 \cdot 5^{3} \cdot 61 \) |
\( 2^{2} \cdot 5^{28} \cdot 61 \) |
$1.98603$ |
$(a+1), (-a-2), (2a+1), (-6a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.190189111$ |
3.043025785 |
\( \frac{14365511976455982039}{5817413330078125} a + \frac{67999514081753286571}{11634826660156250} \) |
\( \bigl[1\) , \( 1\) , \( i\) , \( 1385 i + 1089\) , \( -2956 i + 24961\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(1385i+1089\right){x}-2956i+24961$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
